Variable impedance coaxial device with relative rotation between conductors



J. E. CRUZ Dec. 17,1968

VARIABLE IMPEDANCE COAXIAL DEVICE WITH RELATIVE ROTATION BETWEEN CONDUCTORS 2 Sheets-Sheet 1 Filed Sept. 13, 1965 INVENTOR Jase E. Cruz ATTORNEY Dec. 17, 1968 J. E. CRUZ 3,417,350

VARIABLE IMPEDANCE COAXIAL DEVICE WITH RELATIVE ROTATION BETWEEN CONDUCTORS FiledSept. 13. 1965 2 Sheets-Sheet z CHARACTER/571C IMPEDANCE 52 IN ohms 0 1o a0 60 so a m DE6REES INVENTOR Jose I. Cruz ATTORNEY United States Patent O 3,417,350 VARIABLE IMPEDANCE COAXIAL DEVICE WITH RELATIVE ROTATION BETWEEN CONDUCTORS Jose E. Cruz, Boulder, Colo., assignor to the United States of America as represented by the Secretary of Commerce Filed Sept. 13, 1965, Ser. No. 487,029 3 Claims. (Cl. 333--35) ABSTRACT OF THE DISCLOSURE This is a variable impedance coaxial line in which the inner and outer conductors have noncircular cross sections. Relative rotation between the conductors varies the impedance of the line over a selected range.

This invention relates to a variable impedance device and in particular to one comprising a coaxial transmission line with relative rotation between inner and outer conductors.

Recently the development of Time Domain Refiectometry (TDR) has enabled the measurement engineer to obtain information about the broadband impedance characteristics of coaxial lines and components almost at a glance. The TDR systems have been calibrated for accurate measurements of small reflections by the use of fixed coaxial impedance standards. A variable characteristic impedance device is desirable since it would elimimate the inconvenience of inserting and removing fixed standards.

One variable inductance in the prior art includes a straight outer conductor in the form of a circular, tubular member. An inner conductor, in the form of a conductive rod of circular section, is mounted within the outer conductor by means of rotatable cranks and bearings. The inner and outer conductors are arranged for relative movement about an axis that is eccentric to the longitudinal axis of both conductors and is parallel to the direction of extension of the conductors. In practice, by varying the relative position of the conductors as permitted by the rotatable crank, one may obtain a range of characteristic impedance variations of about 2 to l and a corresponding range of inductance variations.

The eccentric line just described has several disadvantages. It will not propagate a pure TEM mode as readily as a coaxial circular line, and the cranks, supporting the center conductor, limit the upper frequency cut-off. The reflections, due to the cranks, would undoubtedly be too large for the line to be calibrated with the TDR system. Again, the electrical path changes as the inner conductor is rotated with respect to the outer and consequently the quarter-wave path changes. At the upper frequencies this change in path length is quite detrimental. Finally, since the line is not coaxial and symmetrical, it is comparatively difficult to fabricate, the mechanism for rotation of the inner conductor is complex, and mating of the external transmission line is diflicult.

Accordingly, it is an object of the present invention to provide a variable impedance device that has a relatively wide impedance range.

Another object is to provide a variable impedance coaxial device that has a lower frequency limit of D0. and an upper frequency limit that is determined by the crosssectional dimensions of the outer conductor.

Another object is to provide a variable impedance device that may be calibrated with circular coaxial lines of calculable characteristic impedance in conjunction with a TDR system. The impedance of this device is also calculable.

It is another object of this invention to provide a variable impedance transforming device having a quarterw'ave electrical length (or odd multiple of one-quarter) that remains constant due to the cross-sectional symmetry.

Still another object is to provide a variable impedance device that is coaxial and symmetrical and therefore relatively simple to fabricate, permits easy rotation of one conductor in relation to the other and permits easy mating of external transmission lines.

In the figures, wherein like numerals designate like parts:

FIG. 1 is a pictorial of an embodiment of the instant invention;

FIG. 2 is a section taken along the longitudinal axis of the embodiment in FIG. 1;

FIG. 3 is a section taken along line 3-3 in FIG. 2; and

FIG. 4 is a plot of the characteristic impedance versus angle of rotation for an embodiment of this invention.

In accordance with the teachings of the present invention, a transmission line is provided wherein an inner conductor, having a noncircular cross section, is positioned axially in an outer conductor, also having a noncircular cross section. One of the conductors is rotated relative to the other to vary the characteristic impedance of the line over a selected range. More specifically, in one embodiment the inner and outer conductors have a rectangular cross section, and the outer conductor is rotated relative to the inner, which is stationary.

With reference to the figures, arms 10 and 11 are supported on base 12 to form a cradle. Bearings 15 and 16 are positioned in arms 10 and 11, respectively, and coupling units 17 and 18 are located on bearings 15 and 16, respectively. The rectangular outer conductor 19 of the coaxial transmission line 20 comprises upper and lower plates 21 and 22 (FIG. 2), end plates 23 and 24, and side plates 25 and 26 (FIG. 3). The plates are fastened together, by means of set screws to form the outer conductor, and the end plates 23 and 24 are fastened to bearings 15 and 16, respectively, by suitable means not shown. The rectangular inner conductor 30 is located coaxially with the outer conductor and is held in position by means of insulators 31 and 32 in coupling units 17 and 18, respectively.

A gear-scale 35 is attached to bearing 16 and pointer 36 (FIG. 1) is attached to arm 11. The scale is driven, through knob 37 and worm screw 38, over a range greater than degrees.

In one embodiment of variable impedance line 20, the parameters selected were as follows: w/ 12:0;650 and t/b=0.295 with b=0.750". The width D, being greater than 3b, was considered infinite and did not contribute to the characteristic impedance Z. (See the insert in FIG. 4 which defines, by illustration, w, b, t, and D. In the insert, the inner conductor 30 is shown rotated relative to the outer conductor 19 so that the angle 0 may be conveniently represented.)

The characteristic impedance of this variable impedance line was measured as a function of angle of rotation by means of a TDR system. Calibration of the system was accomplished by means of circular coaxial standards whose characteristic impedances were determined from ln a Z is the characteristic impedance of the circular coaxial line.

After the characteristic impedance, Z of the fixed standard was determined, the reflection coefficient, T was calculated from the relationship l s| s o) s+ 0) where Z is a theoretical characteristic impedance which in this case was 50.00 ohms. All subsequent reflection coeflicients were also determined with respect to the same SO-ohm level.

If the reflection coefficient I is known, I,,, the unknown reflection coefiicient of the variable impedance line can be determined from the ratio Here [2 is the amplitude of the reflected voltage corresponding to the reflection coeflicient P and 12 is the amplitude corresponding to the reflection coeflicient, I

Using a known standard reflection coeflicient, P the unknown reflection coeflicient, I,,, was obtained by first measuring the ratio b /b with the TDR system and then inserting the measured value into (3). Although the absolute value of the reflected voltages is ditficult to determine, the ratio of the two such voltages in the same system can be found very accurately. The relative magnitudes of the reflected voltages of both the fixed standard and the variable line standard (as a function of the angle 6, between the inner and outer conductors) were measured and recorded and values of l were obtained as described. Equation 2 was then used to determine the characteristic impedance of the variable line as a function of 6.

FIG. 4 shows the measured results for the variable impedance line 20 detailed above. Examination of the data indicates that the characteristic impedance for this symmetrical configuration is periodic. The step discontinuities at the ends were compensated for experimentally. Thus as the outer conductor 19 is rotated from H= through l9=100 the characteristic impedance of the variable impedance line 20 varies from a little less than 55 to 44 ohms.

The variable impedance rectangular line described here is analyzed in detail in a paper entitled A Variable Characteristic Impedance Rectangular Transmission Line by R. L. Brooke and J. E. Cruz, which was published in IEEE Transactions on Microwave Theory and Techniques, vol. MTT13, No. 4, pp. 477-478, July 1965. In this paper a matrix equation is developed for determining the inductance and characteristic impedance of the rectangular line. A solution of the matrix equation is obtained by computer methods, yielding a convergent numerical result for any cross-sectional dimensions and for any angle of rotation between the inner and outer conductors.

It can be shown that when w/ b is approximately equal to 1, t/ b is equal to 0.05 and D is greater than 3.5b, the variable impedance line described here has a characteristic impedance range of 60 to 1. This line will transmit a pure TEM mode at least as well as a coaxial circular line. The operating frequency of the line has a lower limit of DC. and an upper limit which is determined by the crosssectional dimensions of the line.

The instant variable impedance line can be used as a variable inductor and can also be used as a variable impedance quarter-wave length matching section. When employed as a variable inductor, the inner and outer conductors 30 and 19 are connected together at one end. When employed as a quarter-Wave length matching section, two insulated plates are positioned between inner and outer conductors to make the overall length of the line one-quarter of a wavelength or an odd multiple thereof. This arrangement may be used to effect impedance transformation in accordance with conventional principles. As the line is varied over its impedance range, its quarter-wave electrical length (or odd multiple of onequarter) remains constant due to the coaxial cross-sectional symmetry.

Obviously many variations of the present invention are possible in the light of the above teachings. It will be apparent, for example, that the inner conductor 30 could be made rotatable and the outer conductor 19 could be stationary. The cross sections of the inner and outer conductors could be any one of a number of configurations, e.g., elliptical or triangular, but not circular. It is therefore to be understood that within the scope of the appended claims, the invention may be practiced otherwise than as specifically described.

What is claimed is:

1. An electrical device comprising:

a first coaxial line having an inner and outer conductor, each having a noncireular cross section,

at least one second coaxial line including an inner and outer conductor, each having a circular cross section, means for connecting the inner and outer conductor of said first coaxial line to the inner and outer conductor, respectively, of said second coaxial line,

means for holding the inner conductor of said first line in a stationary position,

means for rotatably mounting the outer conductor of said first line, driven means connected to the outer conductor of said first line, a fixed member, driving means positioned on said fixed member and in engagement with said driven means, and

means for operating said driving means, whereby the characteristic impedance of the first coaxial line is varied as a funtcion of the angle of rotation of its outer conductor.

2. The device set forth in claim 1 including:

a scale,

means for rotating said scale in dependency upon the rotation of the outer conductor of said first line, and

a stationary reference member positioned relative to said scale.

3. The device set forth in claim 1 wherein:

the cross section of the inner and outer conductor of said first coaxial line are each substantially rectangular.

References Cited UNITED STATES PATENTS 2,405,437 8/1946 Leeds 33335 2,728,051 12/1955 Rose 33335 2,433,368 12/1947 Johnson et al. 33335 HERMAN KARL SAALBACH, Primary Examiner.

C. BARAFF, Assistant Examiner.

US. Cl. X.R. 33373, 31, 32 

